A glider, traveling at various speeds, passes two contacts separated by dx=one foot. If traverse takes dt=2 nanoseconds (ns), clocks moving with the glider say that only dT=1.732 ns have elapsed! Here, the letter "d" precedes each variable name to denote "change in". If traverse takes dt=1.5 nanoseconds, glider clocks say that dT=1.06 ns elapsed. If traverse takes dt=1.15 ns, glider clocks say that dT=0.575 ns elapsed. If traverse takes dt=1.06 ns, glider clocks say that dT=0.353 ns elapsed. As you can see, when glider speeds approach one foot per nanosecond, the "speed of glider time with respect to map time" (dT/dt) begins to decrease! But what rules of decrease are suggested by this data? Does this explain why everyone should carry their own watch? And what other
consequences might those rules have...
Discover it yourself: Map-based motion at any speed.
This page is one step in a personal journey to discover 20th century methods for describing motion. It is designed like a multiple choice MAZE with challenges along the way that depend a good deal on the strategies that YOU adopt. Although the questions may look simple, they are designed to lead you toward deep understanding quickly. For example, if you think through in your own way the first three challenges in the series, you will have everything needed to derive all kinematic consequences of the special theory of relativity, and put it through some experimental tests as well. Subsequent challenges will draw out consequences for accelerated motion, and even a quantitative look at simple spacetime curvatures, all from the vantage point of a single map-frame before the complications of multiple reference frames are explored.